Question

Which of these choices show a pair of equivalent expressions? A.7^5/7 and (√ 7)^5 B.6^7/2 and (√ 6)^7 C.(4√ 81)^7 and 81^7/4 D.5^2/3 and (√ 5)^3

Answer 1

We will use the following law of indices (or 'index law') to check each pair of expression

$x^{ \frac{m}{n}} = ( \sqrt[n]{x} )^{m}$

With fractional power, the denominator is the root and the numerator is the power of the term. When the denominator is 2, we usually only write the normal square symbol (√). Denominator other than 2, we usually write the value of the root, for example, the cubic root ∛

Option A - Incorrect
$7^{ \frac{5}{7}}$ should equal to $( \sqrt[7]{7} )^{5}$

Option B - Correct
$6^{ \frac{7}{2} }$ does equal to $( \sqrt{6}) ^{7}$

Option C - Incorrect
$4( \sqrt{81} )^{7}$ should equal to $(4)( 81^{ \frac{7}{2} } )$

Option D - Incorrect
$5^{ \frac{2}{3} }$ should equal to $( \sqrt[3]{5} )^{2}$

Answer 2

C and D

Step-by-step explanation: